Crystals. 129 



crystallography its present form, in all essential points, as a pure science, 

 and subsequent progress has been along the lines of working out details 

 rather than modifying its foundations. 



The accompanying table, (page 130), will shew at a glance the six 

 systems of crystallization now recognized, with their principle synonyms 

 and examples of minerals for each system. 



Very often crystals are met with in which one or more parts are 

 reversed with regard to the others, often presenting the appearance of 

 two crystals symmetrically united. These are termed twin crystals, but 

 the theory of their formation is too elaborate to be gone into in the 

 present paper. Time will not permit me, either, to go into details 

 respecting the various methods of designating the faces of crystals by 

 numbers or symbols, and of calculating their angles. That of Naumann 

 is, perhaps, the one most employed. This subject belongs, however.more to 

 pure geometric crystallography, and will be found fully explained in the 

 text-bocks. I can only briefly mention here some of the many wonderful 

 physical properties possessed by crystals. 



The researches of Brewster on polarized light have already been 

 referred to. The discovery that the shape of the cleavage-form is 

 intimately related to the action of the crystal upon light is due to him ; 

 and his researches, as already mentioned, confirmed the existence of 

 the two additional systems of crystallization recognized somewhat doubt- 

 fully by.Mohs. 



One of the most remarkable discoveries of recent times was the 

 mathematical demonstration by von Lang, Quenstedt, and others, that 

 six, and only six, systems of symmetry are possible for all crystallized 

 matter. 



In 1822, Mitscherlich announced his discovery of isomorphism, the 

 property which substances analogous in chemical composition possess 

 of crystallizing in forms closely resembling each other, and with only a 

 slight difference between their corresponding angles. A good example 

 is siderite and dolomite, the crystal form being a rhombohedron. 

 Mitscherlich also pointed out that the same substance (simple or 

 compound) may crystallize in two distinct systems (dimorphism), or even 

 in three or more (trimorphism and polymorphism) Thus the sulphide of 

 iron crystallizes in the isometric system ( pvrite), and also in the 

 orthorhombic system {marcasite). 



